Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ3
By James E. Colliander, Markus Keel, Gigliola Staffilani, Hideo Takaoka, Terence Tao. 2003
194 citations recorded by the source corpus.
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ca28a5464f81f3e354efa7f9766106051e578ed0
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Rowan Killip
- Gigliola Staffilani
- Justin Holmer
- Svetlana Roudenko
- M. Vi
- Xiaoyi Zhang
- Thomas Duyckaerts
- A. Ionescu
In Control and Systems Engineering
- Xiaoyi Zhang
- Rowan Killip
- M. Vi
- Svetlana Roudenko
- Justin Holmer
- Gigliola Staffilani
- Thomas Duyckaerts
- A. Ionescu
In Mathematical Physics
- Rowan Killip
- Xiaoyi Zhang
- Carlos E. Kenig
- B. Dodson
- M. Vi
- Gigliola Staffilani
- Justin Holmer
- Monica Visan
Citations in the corpus
- Scattering for the non-radial 3D cubic nonlinear Schroedinger equation (2007, background): “In this case, scattering is already known, as a consequence of Morawetz [6], or interaction Morawetz [ 4 ] inequalities.”
- Nonlinear Schrodinger Equations at Critical Regularity (2013, methodology): “As noted above, this is in [19] when d = 3.”
- Semilinear Schrödinger flows on hyperbolic spaces: scattering in H1 (2008, background): “Remark 1.3. The conclusion of Theorem 1.1 (b) is in sharp contrast with its Euclidean analogue: on Euclidean spaces scattering to linear solutions is only known for exponents σ ∈ (2/d,2/(d − 2)), see [23, 35, 20 , 19, 43], and also for σ = 2/(d − 2), see [11, 21, 40, 37, 45].”
- On Blow-up Solutions to the 3D Cubic Nonlinear Schrödinger Equation (2010, methodology): “The argument of Ginibre-Velo has been simplified using a new “interaction Morawetz” identity by Colliander-Keel-Staffilani-Takaoka-Tao [3].”
- On the Cauchy problem of 3-D energy-critical Schrödinger equations with subcritical perturbations (2006, background): “An example of such a priori estimate on which our analysis relies is the interaction Morawetz inequality which has appeared in [7,8], etc.”
- A Sharp Condition for Scattering of the Radial 3D Cubic Nonlinear Schrödinger Equation (2007, methodology): “scattering has been established for all H 1 solutions (regardless of “size”) even for nonradialdatabyGinibre-Velo[11]usingaMorawetzinequality.Thisproofwassimplified by Colliander‐Keel‐Staffilani‐Takaoka‐Tao [ 4 ] using a new interaction Morawetz inequality they discovered.”